The Hamiltonian of the system of bosons ($a$, $a^{\dagger}$, $b^{\dagger}$ & $b$ are Bose operators) is: \begin{equation} H=\epsilon_{1} a^{\dagger}a+\epsilon_{2}b^{\dagger}b+\frac{\Delta}{2}\left(a^{\dagger}b^{\dagger}+ba \right) \end{equation}
where $\epsilon_{1}$, $\epsilon_{2}$, and ${\Delta}$ are real and positive, ${\Delta}$ < ($\epsilon_{1}$ + $\epsilon_{2}$). I am trying to find a Canonical Transformation to diagonalize this Hamiltonian. And afterward to find expressions for the eigenenergies and parameters of the transformation. I am not sure whether first I need to switch to any other space like momentum etc and using Bogoliubov Transformation. Any help and hint will be highly appreciated.